A solenoid is a coil of insulated wire wound on a rod made of solid iron or solid steel.
Due to Lenz's law of induction, the current carrying coil generates a magnetic field which in turn gives the solid iron core magnetic polarity. If you face one end of the solenoid and the current is traveling in a counter-clockwise direction in that face of the solenoid then that end is a north pole. So using your right hand you would curl your fingers in the direction of the current. If when you curl them they go anticlockwise you have a north pole; if when you curl them you go clockwise you have a south pole. The reference links show the corkscrew rule and right hand rule which are other ways of determining the polarity of an solenoid electromagnet using the hand.
Solenoids are used to make transformers.
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